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An approach for design optimization of helical gear pair with balanced specific sliding and modified tooth profile

  • Paridhi Rai
  • Asim Gopal BarmanEmail author
Industrial Application
  • 90 Downloads

Abstract

A unique perspective in design optimization of helical gear pair has been emerged and presented in this article. Specific sliding needs to be balanced for enhancing wear and scuffing resistance of helical gears. Optimized modification in tooth profile has immense benefits in gear operations. Effect of profile shift and specific sliding on design optimization of helical gear pair have been studied and found to be beneficial of great importance. Preventing undercutting, balancing of wear and bending fatigue strength and centre distance adjustment are some of the advantages of profile tooth modifications. Real-coded genetic algorithm (RCGA) has been used to attain minimum volume of helical gear pair. Profile shift coefficients for gear and pinion have been included as design variables along with mostly used generic design variables, module, face width and number of teeth on pinion. Specific sliding, transverse contact ratio and face width constraint along with other strength requirements are the design constraints. The optimal design solutions obtained with and without profile shift are recorded and compared with commercially used software for validation. 3D computer-aided design (CAD) models have been developed by using the optimized results obtained from RCGA and commercially used software. These CAD models are used for performing finite element analysis (FEA) on the helical gear set for analyzing the stress developed in the gear pair. The developed stress in the helical gear pair is found to be well within the allowable stress limits for the gear pair.

Keywords

Helical gear Profile shift Specific sliding Volume optimization Real-coded genetic algorithm FEM analysis 

Abbreviations

b

Facewidth

\(d_{a_{1}}\)

Pinion tip diameter

\(d_{a_{2}}\)

Gear tip diameter

i

Transmission ratio

Ft

Tangential load

KA

Application factor

KFα

Transverse load factor (bending stress)

KFβ

Face load factor (bending stress)

KHα

Transverse load factor (contact stress)

KHβ

Face load factor (contact stress)

KV

Dynamic factor

m

Normal module

mt

Transverse module

N1

Pinion rotational speed

rb

Base diameter

T

Torque

tst

Starting time

V

Volume of helical gear pair

x1

Pinion profile shift

x2

Gear profile shift

YF

Form factor

YNT

Life factor

YST

Stress concentration factor

Yβ

Helix angle factor

ZB

Single pair tooth contact factor (Pinion)

ZD

Single pair tooth contact factor(Gear)

ZE

Elasticity factor

ZH

Zone factor

ZL

Lubrication factor

z1/z2

Number of teeth on pinion/gear

Z𝜖

Contact ratio factor

Zβ

Helix angle factor

ρ

Density

σFP

Nominal permissible bending stress

σHP

Nominal permissible contact stress

σFlim

Allowable bending stress

σHlim

Allowable contact stress

αt

Transverse pressure angle

𝜖α

Transverse contact ratio

Subscript

1

Pinion

2

Gear

Notes

Acknowledgements

The authors would like to thank Mr. Chinmay Joddar, Manager - Design and Development, New Allenberry Works, Kolkata, India, for helping in validation part with commercially used software.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringNational Institute of Technology PatnaPatnaIndia

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